Frequency of a particle? Frequency of what?

Okay, I have a quantum physics problem set, and I would really like to have a clear understanding of what I'm doing before I get into the thick of it.

This is probably incredibly cliche, but I'm having trouble understanding particle-wave duality. I have no problem with the concept of a particle exhibiting wave-like features; however my teacher and textbook are very ambiguous about the frequency and wavelength of particles.

I have no problem with the fact that a photon, an electron, or whatever have frequency, considering that different colors exist :D and other such examples. I'm just not exactly clear on what exactly the frequency is measuring.

So, frequency is defined as the number of cycles per second. My question is in relation to particles "cycles of what?"

So, a wave (as in, ones found at the beach) frequency is measured by number of waves that go by per second. Sound is measuring change in pressure. (I appologize for poor use of words, but please try to understand what I'm getting at.) Then when I get to particles, frequency of a particle is... uh... what?

As I said, I have no problem with the fact that frequency of a particle exists. I have a problem with exactly what the frequency is measuring. Frequency of a particle is the number of cycles of _______ per second. I'm wondering what goes into that blank spot.

Thank you for considering my question and such, I know it probably seems silly, but I honestly can't find a straight answer for this question.

The peaks are in the probability distribution of where you are likely to find the particle if you measure its position. Only if you know the momentum perfectly, and thus have maximum uncertainty about the position, will the distribution look like a plane wave where the peaks are equal in size in all directions off to infinity (each possible momentum corresponds to a unique frequency for any given particle); if you've localized the position enough so the probability distribution has a "hump" in it, then by fourier analysis this can be treated as the sum of a lot of plane waves with different possible frequencies, and thus a lot of possible momenta.

The peaks are in the probability distribution of where you are likely to find the particle if you measure its position. Only if you know the momentum perfectly, and thus have maximum uncertainty about the position, will the distribution look like a plane wave where the peaks are equal in size in all directions off to infinity (each possible momentum corresponds to a unique frequency for any given particle); if you've localized the position enough so the probability distribution has a "hump" in it, then by fourier analysis this can be treated as the sum of a lot of plane waves with different possible frequencies, and thus a lot of possible momenta.

Careful Jesse; the wavefunction for a given momentum is something like exp[ip.x] --- which has constant modulus over all space and time. Specifically, there is exactly no spatial variation in the probability density. What you've written sounds almost like there is a plane-wave distribution for the probability density, which isn't true.

Careful Jesse; the wavefunction for a given momentum is something like exp[ip.x] --- which has constant modulus over all space and time. Specifically, there is exactly no spatial variation in the probability density. What you've written sounds almost like there is a plane-wave distribution for the probability density, which isn't true.

Ah, so it's only a spatial variation in the phase? I haven't studied this stuff in a while...